Why So Negative On These Unintended Consequences?

From Slate:

Nebraska is the last state to pass a so-called "safe haven" law designating places such as hospitals or police departments where a parent can give up one or more children without risking jail time.

Unlike the laws passed in the other 49 states, where typically the child must be one month old or less, Nebraska's measure imposes no age limit; infant and strapping teenager alike may be forfeited. As a result, Nebraska is turning into a national dumping ground for unwanted kids. Mothers and fathers eager to cull their herds have shown up from distant Michigan, Arizona, Georgia, and Iowa. In one busy 24-hour period in September, 11 children were deposited at local hospitals, including nine siblings left by a single father. One 16-year-old girl didn't even know she was being abandoned. Concluding, sensibly, that the Nebraska law as written is disastrously broad, Gov. Dave Heineman has called for a special legislative session this month to cap at three days the age of lawfully abandoned children.

I don't understand the controversy here, maybe someone can offer help. Nebraska, like many others, are trying to avoid the unintended consequences of having laws that jail parents for abandoning their children (that I prefer not to imagine). As a result, they create a safe haven to overcome these, but they are upset over the scale? The author says the conclusion the law is "disastrously broad" as being "sensible," but it is not at all clear to me.

I have to imagine that most good parents are not near the margin of dump or keep, but instead face a large discrete jump. Children whose parents are near the margin I would guess have a fairly unhappy home life, regardless if it is 1 month or 16 years. Alternatively, the parent may be extremely loving but has so much concern over their own ability to raise a child it overwhelms their instinct to keep them.

In either of these two cases, how does restricting the safe haven laws make anyone better off by forcing them to remain in the situation? It is not obvious to me, the comments are open as always.